I don't think so. That looks like a small cardboard box with some kind of label on it.
Well, it could be a box.
One important question is whether or not Earhart carried a compact on the world flight.
There is some evidence from a newspaper account she did.
Ricker wrote on June 20, 2012:
"A quote below is from Melbourne's The Argus newspaper's article describing Earhart's arrival in Darwin, remarking that she powdered her nose before she exited the Electra. Interestingly, there was also a photo taken in Darwin at that time which captured AE on the wing of the Electra with an item in her hand which looks like it could be a compact. The photo was published in the Adelaide The Mail
in a story following the failed flight.
'Her navigator, Captain Fred J. Noonan, began to move from
the cockpit of the machine-"the flying laboratory"-as
the engines were shut off. But Mrs. Putnam pulled him
back. Then, nonchalantly producing a puff, she powdered
her nose before stepping out of the cockpit to wave
cheerily to the crowd. Her slide down the wing to the
From The Argus (Melbourne, Vic. : 1848-1954), Tuesday 29 June 1937, page 9
Ricker, Tom and I have no basis to know whether or not any of these compact tales are true, but it's easy to understand why we think they may be true.
The photo and the story of AE "producing a puff" before deplaning could well have been referring to the same place and time, the Darwin arrival while on the wing of the aircraft, and therefore could well refer to the object AE is holding in the photo.
It's not unassailable. It's simply a reasonable possibility, probably to be no more than that, but it's the kind of thing I always find intriguing.